Was hired as a temporary employee (not through an agency) for one year and was told by HR that maybe after 6 months they would consider bringing me on FT. Would it be better to express my interest with HR instead of my manager since they were the ones who originally mentioned it?
Go to your manager first. You need all the allies you can get. Especially if your manager is a good person who wants to support you, they need some time to prepare mentally to push against HR.
Plus typically line managers don’t set the budget, so making a team member permanent will be in their own interest, unlike HR who might be instructed to keep the cost down.